The essence of logic is to find out what argumentative structures

[Mentat]

Originally posted by Tom
It was tough, but I actually resisted the urge and did not log on once the entire long weekend.

I just can't believe it!

Anyway, I'm glad you're back, as I'd like to keep working on this thread.

It can't be an A statement, because that is the "Universal Affirmative" statement, and 60% of a whole is not universal. This is a tricky one, because it is a combination of two types, I and O. That is, it expresses the I statement...

Some college students work part-time to pay for their education.[/color]

...but not exactly. That is because the logical quantifier "some" includes the case of "all". But, we are told a very specific "some" (60 percent) that most definitely does not include "all". So, the above also expresses the O statement...

Some college students do not work part-time to pay for their education[/color]

This is called an "exceptive statement", and is discussed in the Logic Notes in the 12th post from the top (do a "control-F" for the word "exceptive" and you'll be taken right to it).

I see. I'll go look that up ASAP.

Almost. It is another exceptive I + O statement. "Almost all" communicates the idea that it is "some but not all"

Hmm. I was close though .

Right. I would even go so far as to say that it is two[/color] E statements:


War is not healthy for children.
War is not healthy for other living things.
[/color]

Since the predicate is compound, so is the statement. But, since we are not on Quantificational Logic yet the distinction is not yet important.

Interesting point.

 

[Mentat]

Tom,
I just looked up that part on exceptives, and I have a question:

Why must a statement be considered exceptive, merely because it can be both an I statement or an O statement? After all, it seems that any I statement has an inverse form that is in the form of an O statement.

What I mean is: Doesn't any statement of the form "some p are q" always imply that "some p are not q" (otherwise, it would not be "some p are q" but "all p are q" (an A statement)). Please help me out on this whenever you have time.

 

[drnihili]

Originally posted by Mentat
Tom,
I just looked up that part on exceptives, and I have a question:

Why must a statement be considered exceptive, merely because it can be both an I statement or an O statement? After all, it seems that any I statement has an inverse form that is in the form of an O statement.

What I mean is: Doesn't any statement of the form "some p are q" always imply that "some p are not q" (otherwise, it would not be "some p are q" but "all p are q" (an A statement)). Please help me out on this whenever you have time.

I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to check to see whether other people have beards. And the I statement remains true even if we should later discover that all contributors have beards.

Now it's true that we don't typically make an I statement if we know that the A statement is also true. It would sound odd to say "Some whales are mammals". But this isn't because saying it would be false. Instead it's because there are rules of conversation that encourage us to give as much information as we reasonably can. THis sort of thing is generally taken care of in the field of pragmatics. Specifically, the requirement to not assert an I statement when you know the corresponding A statement to be true is part of the theory conversational implicature developed by Grice.

 

[Mentat]

Originally posted by drnihili
I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to check to see whether other people have beards. And the I statement remains true even if we should later discover that all contributors have beards.

Now it's true that we don't typically make an I statement if we know that the A statement is also true. It would sound odd to say "Some whales are mammals". But this isn't because saying it would be false. Instead it's because there are rules of conversation that encourage us to give as much information as we reasonably can. THis sort of thing is generally taken care of in the field of pragmatics. Specifically, the requirement to not assert an I statement when you know the corresponding A statement to be true is part of the theory conversational implicature developed by Grice.

Thank you for that, drnihili. That makes perfect sense now.

 

[HeavensWarFire]

UUMMMMM


I couldn't help but to realize what looks to be an error in judgement:

I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to check to see whether other people have beards. And the I statement remains true even if we should later discover that all contributors have beards.

I am not sure the admission a of a single contributor having a specific charactoristic is the same as the term "some." "Some" seems to imply more than one, to what degree exactly, no one knows, hence, the use of the word "some" for a generally unknown amount of something; but how can you infer that some have beards simply because you have found a case of a single person actually having a beard? Does a single person constitute a "some" in the strickest sense?

I understand the term "some" to be of an undefined amount of something, but the some is more generally than a single case.

Take for example the following analogies.

A person arrives to a party, and they are asked by someone else if they have gotten a portion of a cake, to which they reply, "Yes, i got some cake."

In the case above, we really don't know what is meant by "some." What is the some? A bite? An actual slice? Or a crumb?

In the example of "some Ps are Qs" the word "some" is not all exclusive, hence, it would follow then that "some Ps 'are not' Qs" since you did not use an all exclusive term.

An all exclusive term would be something like, "all" or "unexceptionally" since you are not really leaving room for any kinds of deviations, or alternatives.

A true law, a true rule, would be an axiom that you can not really find an exception for. Which brings us to the paradox of whether or not a rule is the exception, rather than the actual rule. Maybe some rules are the exceptions rather than the standard, no?

 

[HeavensWarFire]

Part 2



This doesn't sound correct either:

Now it's true that we don't typically make an I statement if we know that the A statement is also true. It would sound odd to say "Some whales are mammals". But this isn't because saying it would be false.

But it is a missuse of language, since, the very idea of a mammal is a pretty well defined term. Hence, if you say some mammals are whales, then by default you are allowing for the possibility for one to think that some whales 'are not mammals,' hence, it would in fact be false to make such a statement, if it is the case that all whales are mammals, unexceptionally.

Certain terms, exclude other ideas automatically. This is what gives language in some instances the power to establish resolution to a problem.

Take for example, the notion, that an "unstoppable truck can break, and be stopped by an unbreakable wall."

You are having a collisions of concepts that can not be logically sound due to the terms being used, and justapose.

If a truck is really "unstoppable," then it must either move a wall, or break a wall, but you can't break a wall that is "unbreakable." Hence, you are logically at a stand still, since you have ran into a contradiction that can not logically hold to be true when it juggles 2 highly oppositional ideas. One or the either of the main predicates of a sentence must be true, but you can't have 2 predicates of opposing meaning to be true.

This is why it gets hard to explain the whole idea of "an unmoved mover," or a big bang.

If there is nothing to cause the motion of an object, then why wouldn't it be the case that the object will remain stationary if there is nothing else to act on the object?

How could GOD be a self-sustained mover, if all things require a mover to set them into motion?

What caused GOD to be, if GOD is the cause of everything else?

Why would something that was once a huge blob of hydrogen, all of the sudden, after an immense amount of time of just being a big blob explode upon itself, and spring a Universe from its raw materials?

Doesnt make sense.


To think there was a time, when the blob was just a blob, not murmuring, not moving, not having any kind of activity, and then all of the sudden, it has activity, like a particular molecule moving from its stationary position until it bumped into another, and that in turn bumped into a third, until kaboom, you had this mass population of atoms bouncing off each other to the point where, kaboom, it all just exploded, then the main question becomes as to what caused the first domino to fall so that it would then knock over all the remaining dominos?

Dont make sense.

If all things are stationary, then how can any movement commence?

Something must have either been in motion by accidant always, and thus the cause all other motions. Or there must have been something that "had the will" to be the exception to the rule with regards to all things being still, and in a concentrated location.

Life is a grand Mystery. Kinda like GOD. Neither one of them make sense really. But then again, Immanual Kant was wrong, and David Human right. We do impose our ideas onto life. The idea of order is a human concept that has no real basis in reality.

 

[drnihili]

Those are good points about the use of language. The question is whether they are in the realm of logic or in the realm of pragmatics. The standard answer is that they are issues of pragmatics. The seminal piece on this issue is H. P. Grice's "Logic and Conversation". If the issue interests you and you're near a decent library, I recommend the anthology Pragmatics: A Reader edited by Steven Davis. It contains Grice's paper and many others.

I don't have time at the moment for a point by point response, but I'll try for that later today.

nihili

 

[Evo]

I confess that I have only just begun to read through the posts, but I notice that people seem to be overthinking things.

Logic is simple, it shouldn't be this hard to grasp.

Tom, great information on logical declarative sentences. Takes me back a few years.

In my experience, people either are capable of logical thinking, or they're not.

 

[logicalroy]

Sure, but you'll probably recognize it, before I'm through.

The paradox of Deductive Logic
Let's take, for example, Euclid's rule: "If two sides of a triangle are equal to the same, they are equal to each other" (I think that's how it goes).

For the purpose of this example, let's say that there is a triangle, where it can be shown that the two sides are equal to the same, but I refuse to believe that they are equal to each other.

Now, you would wish to use deductive logic to show me that it must be so, but...

Proposition 1 is "The two sides are equal to the same"
Proposition 2 is "If two sides are equal to the same, they are equal to each other"

Now, I'll accept those two, but it is another proposition altogether (Proposition [oo]) to say that "Therefore, the two sides are equal to each other". I refuse to accept Proposition [oo], and have no reason to yet. So, you say, "if you accept Propositions 1 and 2, then you must accept Proposition [oo]", which we'll call Proposition 3.

Well, now I'll agree to Propositions 1, 2, and 3, but I still disagree with Proposition [oo], and I don't have to agree with it, because you have yet to say that "if you accept 1, 2, and 3, you must accept Proposition [oo]".

And so it goes on. This is an Inductive approach, in that I am telling you that, no matter how many new propositions you produce, you will still never resolve this paradox.


The paradox of Inductive Logic
This is much more simple. Basically, deductive logic tells us...

1) Inductive Logic is based on learning from observed patterns.
2) What we think is a "pattern" is not necessarily a pattern (it could be a coincidence every time) unless you have tried it as many times as possible (which is infinite, obviously).
3) Therefore, Inductive Logic is based on trying something an infinite amount of times, and is thus not "proof" of anything.

Thanks. It's very interesting to me.

Yeah, I've had some dealings with symbolic logic before (mostly in Raymond Smullyan's books, which I highly recommend, btw), and I think it's probably one of the most interesting things I've studied.

You must be kidding! Dude, you have not proven there to be any paradoxes with DEDUCTION. You simply don't know enough. You are confused. You erroneously beieve you accepting the premises has something to do with OBJECTIVE truth. You wrote: "Now, you would wish to use deductive logic to show me that it must be so, but...
Proposition 1 is "The two sides are equal to the same"
Proposition 2 is "If two sides are equal to the same, they are equal to each other"
Now, I'll accept those two, but it is another proposition altogether (Proposition [oo]) to say that "Therefore, the two sides are equal to each other". I refuse to accept Proposition [oo], and have no reason to yet"
THAT'S because you are crazy! Your first premise isn't a complete sentence to begin with. The second makes more sense than the first, but what does "the same mean?" From what I gather in your example, proposition [oo] would be a conclusion in your example. If the premises are true then the conclusion MUST be true. That's like saying: "I don't agree that Roy has a sister; therefore Roy can't have a sister." Get over yourself! You not accepting the conclusion HAS NOTHING TO DO WITH LOGIC. You must see a psychologist for that. In this world there are OBJECTIVE FACTS and they will be true whether you agree with them or not. For example, it is an OBJECTIVE FACT that here on Earth ALL trees are a form of plantlife. Does that need your agreement to be true? No offense, but most people have the wrong ideas about LOGIC of which I am formally trained. I am not self taught. You are like most beginners who do not know the difference between PSYCHOLOGY and PHILOSOPHY. You am a majority of people who post here are confusing the two subjects. PHILOSOPHY is NOT a branch of PSYCHOLOGY where we can just sit around and express our emotions, thoughts and beliefs. That is what a psychology forum should be about. You are in a PHILOSOPHY forum correct? Learn something about REAL PHILOSOPHY. Philosophy is not just a belief or an opinion like most beginners believe. Here is a PROFESSIONAL LINK to where there are people who have PHD in PHILOSOPHY and answers questions like your for free:http://www.shef.ac.uk/uni/projects/ptpdlp/questions/feedback/feedback.html . Scroll down to "SUBMIT QUESTION" or you can read previous answers to questions like yours by going to the "ANSWERS" icon. Once you see what REAL PHILOSPHY is about you will see that sites like this (where anyone can vent their feelings )are a joke. This forum should be labeled "PSYCHOLOGY FORUM" not PHILOSOPY.

 

[Math Is Hard]

Calm down, Roy. Everything's going to be OK. Really.

 

[Les Sleeth]

You must be kidding! . . . You simply don't know enough. You are confused. . . . THAT'S because you are crazy! . . . Get over yourself! . . . You must see a psychologist for that. . . No offense, but . . . You are like most beginners who do not know the difference between PSYCHOLOGY and PHILOSOPHY . . . You are in a PHILOSOPHY forum correct? Learn something about REAL PHILOSOPHY. Philosophy is not just a belief or an opinion like most beginners believe. . . . Once you see what REAL PHILOSPHY is about you will see that sites like this (where anyone can vent their feelings )are a joke.

Here is a PROFESSIONAL LINK . . . .

Thanks for the link, sounds like a real friendly place!

 

[honestrosewater]

Tom, why don't you add your logic notes to your philosophy napster thread- or the links directory (which I just discovered today!)? Can you add internal links to the links directory? BTW I was going to add several links to the directory- many of which are listed other places on PF- no one would have a problem with that, right?